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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Exploring discrete structures in planar graphs through Fáry’s theorem and its combinatorial implications

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pp. 281–288Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2484 Crossmark XML
Received:
07 May 2025
Published Online:
31 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2484
Pages:
281–288

Abstract

This study explores the discrete structures of planar graphs, focusing on Fáry’s Theorem and its combinatory consequences. According to Fáry’s Theorem, all planar graphs may be put in the plane using straight edges (e). This explains how planar graphs are formed (d). This study examines how certain combinatorial elements of this result affect graph theory notions like edge crossing, planarity, and vertex connect. Focusing on Fáry’s Theorem’s relevance to computational geometry and optimization, we examine its impact on graph drawing techniques. The study explores the relationship between Fáry’s Theorem and various combinatorial structures, such as Sterling numbers and graph coloring, to gain insight into planar graph behaviour and grouping. The results help us enhance theory and apply it to network design, circuit planning, and spatial data modelling, where planar graph topologies are crucial.

Keywords

Fáry’s theoremPlanar graphsDiscrete structuresCombinatoricsGraph drawing

Subject Classifications

05C10

References

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